One interesting property of the magnetic twisted convolution is that in addition to the classic Young's inequalities, it also satisfies the following \(L^2\) -inequality [1]} or [2]}
\(\Vert f * g \Vert _{L^2} \leqslant \frac{1}{\sqrt{2\pi }\ell _B}\Vert f \Vert _{L^2} \Vert g \Vert _{L^2} ,\qquad f,g \in L^{2}\big (\mathbb {R}^2\big ) .\) 
